How do I make my game music keep playing between scenes?
Add a manager scene, where stuff should happen independently from other scenes. You can set and remove scenes, but the manager should be kept as it is.
On the manager scene, add an object that receives messages, and each message sets a property named song to a integer number. You know, if a message sensor looking for song_1 message is activated, sets the property song to 1, and so on.
On the same object, make a logic to play each song (on loop stop mode) according to its property number. You know, if property song is 1, play song_1.ogg, and so on.
On each level, make an object send a message at startup to change the song. For example, Always > AND > Message with the subject song_1, and so on according to the level.


If everything went well, when a level restarts and the song is already playing, it shouldn't restart the song, and when the property song changes the object will stop the previous song and start the new one according to the logic.

Using this method of a manager scene also helps to keep everything on only one place, instead of looking for each scene to change the song or whatever.